The reasoning behind Nynaeve's actions is pointed out quite clearly:

"That's why I broke the rules. I thought they were just arbitrary. I couldn't remember why I wasn't supposed to run, so in the face of seeing people die, it seemed silly to walk."

"My goal in this test was to prove that I deserve to be Aes Sedai. Well, then, I could argue that the lives of the people I saw were more important than gaining that title. If losing my title is what would be required to save someone's life—and if there were no other consequences—I'd do it. Every time."

"I wonder if," Nynaeve said, "we sometimes put the White Tower—as

an institution—before the people we serve. I wonder if we let it become a goal in itself, instead of a means to help us achieve greater goals."

"Would you have me choose between a foolish oath and the fate of the world?""

The Aes Sedai claim to serve a higher purpose but most of the time they live in their ivory tower and bicker amongst themselves. Calmly obeying orders is great...if the one who gives the orders has a clue. Nynaeve has proven many times she can cope with extreme situations.

Of course she can, she defeated Forsaken. She does it when she knows and believes in this higher purpose. For a real world analogy - many soldiers would die for their country but wouldn't risk their lives by becoming mercenaries.

No, if there is a tangible goal Nynaeve can choose. It's arbitrary rules she has a problem with. For instance she doesn't go rescue Mat from Ebou Dar or she goes to the WT in Book 2 instead of staying around Rand to help him. If she were that incapable of seeing the bigger picture she would never go fight and would just go around healing people. The whole point is that while trying to save everyone might be too idealistic to work in the real world, sacrificing everything for the sake of an ideal (the WT) can backfire too, especially if this ideal is very far from perfect. A balance needs to be struck.